Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations
In this article, we consider a nonlinear neutral <i>q</i>-fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4763 |
| _version_ | 1797456471656497152 |
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| author | Mouataz Billah Mesmouli Abdelouaheb Ardjouni |
| author_facet | Mouataz Billah Mesmouli Abdelouaheb Ardjouni |
| author_sort | Mouataz Billah Mesmouli |
| collection | DOAJ |
| description | In this article, we consider a nonlinear neutral <i>q</i>-fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, as well as the stability of solutions. Our main results extend and generalize previous results mentioned in the conclusion. |
| first_indexed | 2024-03-09T16:08:18Z |
| format | Article |
| id | doaj.art-a082f4e1579845c1aae1f2c43bbdabe9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:08:18Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a082f4e1579845c1aae1f2c43bbdabe92023-11-24T16:29:17ZengMDPI AGMathematics2227-73902022-12-011024476310.3390/math10244763Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference EquationsMouataz Billah Mesmouli0Abdelouaheb Ardjouni1Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras 41000, AlgeriaIn this article, we consider a nonlinear neutral <i>q</i>-fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, as well as the stability of solutions. Our main results extend and generalize previous results mentioned in the conclusion.https://www.mdpi.com/2227-7390/10/24/4763stability<i>q</i>-fractional difference equationsKrasnoselskii fixed point theoremcontractionArzela–Ascoli’s theorem |
| spellingShingle | Mouataz Billah Mesmouli Abdelouaheb Ardjouni Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations Mathematics stability <i>q</i>-fractional difference equations Krasnoselskii fixed point theorem contraction Arzela–Ascoli’s theorem |
| title | Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations |
| title_full | Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations |
| title_fullStr | Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations |
| title_full_unstemmed | Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations |
| title_short | Stability in Nonlinear Neutral Caputo <i>q</i>-Fractional Difference Equations |
| title_sort | stability in nonlinear neutral caputo i q i fractional difference equations |
| topic | stability <i>q</i>-fractional difference equations Krasnoselskii fixed point theorem contraction Arzela–Ascoli’s theorem |
| url | https://www.mdpi.com/2227-7390/10/24/4763 |
| work_keys_str_mv | AT mouatazbillahmesmouli stabilityinnonlinearneutralcaputoiqifractionaldifferenceequations AT abdelouahebardjouni stabilityinnonlinearneutralcaputoiqifractionaldifferenceequations |